Question

设f(x,y)有一阶连续偏导数,且f(x,x2)=1,f′x(x,x2)=x,求f′y(x,x2)(x2是x的平方)

Answer 1

f(x,x^2)=1

两边对x求导得：

fx(x,x^2)+fy(x,x^2)2x=0

fy(x,x^2)=-fx(x,x^2)/(2x)=-1/2